Feature selection for best mean square approximation of class densities

A criterion for linear feature selection is proposed which is based on mean square apporximation of class density functions. It is shown that for the widest possible class of approximants, the criterion reduces to Devijver's Bayesian distance. For linear approximants the criterion is equivalent to well known generalized Fisher criteria

On the existence, uniqueness, and asymptotic normality of a consistent solution of the likelihood equations for nonidentically distributed observations: Applications to missing data problems

A general theorem is given which establishes the existence and uniqueness of a consistent solution of the likelihood equations given a sequence of independent random vectors whose distributions are not identical but have the same parameter set. In addition, it is shown that the consistent solution is a MLE and that it is asymptotically normal and efficient. Two applications are discussed: one in which independent observations of a normal random vector have missing components, and the other in which the parameters in a mixture from an exponential family are estimated using independent homogeneous sample blocks of different sizes

Sufficient statistics for mixtures of measures in a homogeneous family

Methods for identifying finite mixtures and sets of measures are given. Theorems and corollaries are provided for characterizing sufficient statistics for analysis

On the consistency of the maximum likelyhood estimate of normal mixture parameters for a sample with field structure

General theorems concerning the strong consistency of the MLE of exponential mixture parameters are proved. These theorems imply the strong consistency of the MLE of normal mixture parameters when the data is organized into fields each of which is a random sample from one of the component normal distributions

A Homologous Series of Cobalt, Rhodium, and Iridium Metalloradicals

We herein present a series of d7 trimethylphosphine complexes of group 9 metals that are chelated by the tripodal tetradentate tris(phosphino)silyl ligand [SiP^(iPr)_3]H ([SiP^(iPr)_3] = (2_(-i)Pr_2PC_6H_4)_3Si^–). Both electron paramagnetic resonance (EPR) simulations and density functional theory (DFT) calculations indicate largely metalloradical character. These complexes provide a rare opportunity to compare the properties between the low-valent metalloradicals of the second- and third-row transition metals with the corresponding first-row analogues